Dot product between two vectors $\vec{u}$ and $\vec{v}$ is given by
$\vec{u}.\vec{v}=|\vec{u}||\vec{v}|cos\theta $ where $\theta$ is the angle between both the vectors
If vectors are perpendicular then $\theta=90°$ and $cos90°=0$, i.e $\vec{u}.\vec{v}=0$
Given $\vec{u}=2i+\lambda j+k$ and $\vec{v}=i-2j+3k$
$\vec{u}.\vec{v}$= $2-2\lambda+3=0$
$5-2\lambda=0$
$\lambda= \frac{5}{2}$
Hence option D) is correct